By James E. Gentle
Bioinformatics in addition to Computational Intelligence are unquestionably remarkably quick transforming into fields of analysis and real-world functions with huge, immense strength for present and destiny advancements.
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Extra resources for Bioinformatics Using Computational Intelligence Paradigms
The membership of an element u of a universe U to a subset A can be indicated by a suitable mark in the “list” of all elements u of U . Without loss of generality this mark can be chosen as the number 1 and for ﬁlling up the corresponding column of the list the mark 0 indicates then all those elements u not belonging to the set A. The function generated in this manner is the well-known characteristic function usually denoted by χ: χA (u) = 1 , if u ∈ A, 0 , if u ∈ /A. 11) The basic idea is now the allowence for an element u to belong to a set A also gradually.
A possible model incertainty is neglected in the face of argument impreciseness. The aim of investigation is an assessment of the imprecision of the value y of the function. For that two further assumptions are introduced. On the one hand it is assumed that the function f is diﬀerentiable with respect to its arguments, and on the other hand that the imprecision of the measurements is small when compared with the variations of these derivatives. 2) ∂f In this representation the partial derivatives ∂x are to be interpreted each as j the mean value within the interval ∆xj .
2. A glancing intersection of two straight lines in the plane with the obvious solution (4; −5). Thus an insigniﬁcant changing of the coeﬃcients causes an enormous changing of the solution. This eﬀect is called numerical instability. In the given case the reason for this phenomenon can be explained simply geometrically: The solution of a system of two linear equations with two unknowns is equivalent with the determination of the intersection point of two straight lines in the plane. If the two lines are nearly parallel, then they have a glancing intersection.
Bioinformatics Using Computational Intelligence Paradigms by James E. Gentle